Vettel and David Coulthard will sample a portion of the circuit at an Infiniti event on April 22.
Oleg Zabara, operations director of the Sochi promoter, said work on the track was taking place 24 hours a day.
"I would like to assure everyone that we are completely in line with our schedule," he said. "And we don't see any reason for delay at the moment. Our plan is to finish all works by September 2014."
The only limitations are set by parallel preparations for the Winter Olympic Games, which are due to take place next February. But the clashes with F1 infrastructure are minimal.
"Now the construction project goes with two main directions – track surface is first, while buildings are second," said Zabara.
"The first layer of asphalt has been laid on 60 per cent of the 5.8 km lap. We simply can't do more just now because of Olympic stadiums and pedestrian bridges.
"Then, team buildings, pit buildings, the medical centre and race control tower are all structurally finished. Now it's a time for some facing and inside work on them. The first level of the main grandstand has been also constructed."
Although the exact date of Sochi's maiden grand prix has not yet been confirmed, it is expected to be in September or early October 2014.